# Math Help - The function is defined if...

1. ## The function is defined if...

(e^( cos^(-1) (log x^2) ))^1/2

The base of log is 4

2. Originally Posted by utsav
(e^( cos^(-1) (log x^2) ))^1/2

The base of log is 4
What are you trying to do?

3. Originally Posted by Prove It
What are you trying to do?
The question is: The function is defined if..., we have to find the domain of the given function.

4. Originally Posted by utsav
(e^( cos^(-1) (log x^2) ))^1/2

The base of log is 4
$f(x) = \sqrt{e^{\arccos{[\log{(x^2)}]}}}$.

Note that the logarithm is only defined for $x > 0$.

Since $x^2 \geq 0$, we can already see that we can not let $x = 0$.

Also note that $\arccos{x}$ is only defined for $-1 \leq x \leq 1$.

The exponential function is always $>0$, so there are not any further restrictions for the square root.

Thus the domain is $x \in [-1, 0)\cup(0, 1]$.